Question

Resolve each of the following quadratic trinomials into factors:

15x² - 16xyz - 15y²z²

Answer 1

Here, coefficient of x² = 15, coefficient of x = -16yz and constant term = - 15y²z²

We shall now split up the coefficient of middle term i.e., -16yz into two parts whose sum is -16yz and product is 15 (-15y²z²) = - 225y²z²

Clearly,

-25yz + 9yz = -16yz and

(-25yz) (9yz) = - 225y²z²

So, we replace middle term -16xyz = -25yz – 9yz

Thus, we have

15x² -16xyz- 15y²z² = 15x² - 25yz + 9yz - 15y²z²

= 5x (3x – 5yz) + 3yz (3x – 5yz)

= (5x + 3yz) (3x - 5yz)